Re: How can I proove associtivity of natural in relational algebra?

Filter911 wrote:
> Mikito Harakiri wrote:
> > Filter911 wrote:
> > > Mikito Harakiri wrote:
> > > > Filter911 wrote:
> > > > > Can someone give me a link for a full proof or something?
> > > >
> > > > Given relations A,B, and C, expand each realtion into a (possibly
> > > > infinite) relations A', B', and C' with the same set of attributes
> > > > (which is the union of the attribute sets for A, B, and C). Then, the
> > > > join of A, B and C is the intersection of A', B', and C'. Intersection
> > > > is associative.
> > >
> > > What do you mean by "expand each relation"?
> >
> > "Extend", is the opposite of "project". E.g. the relation with a single
> > attribute
> >
> > A = {(a=1), (a=2)} is exended to the attribute set {a,b} with the
> > domain of attribute b being {7,8,9} as
> Extanding using what? Using B or C? or some new relation? any full
> example or link?
> If I use the union of the three then A=B=C and that's a prviate case

Find the set of all attributes in B and C which are not in A. Get
cartesian product of their respective domains. Cartesian product it
with A. This is how you get A'.